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A323545
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a(n) = Product_{k=0..n} (k^7 + (n-k)^7).
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13
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0, 1, 32768, 79593387129, 328983774635229184, 8781626117710113525390625, 570409595340477623191338982834176, 112244673425189306235795780017831813874289, 49449149324106963036650868175987491957290049732608, 48527312221741371319651099141827554314119977393170380398241
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ exp((8*cos((Pi + arctan(2769*sqrt(3)/239))/6)*Pi/sqrt(21)-6)*n) * n^(7*n+7).
Equivalently, a(n) ~ exp((4*Pi*sqrt(2*(13 + 19*sin(Pi/14) - sin(3*Pi/14))/7)/7 - 6)*n) * n^(7*n+7). - Vaclav Kotesovec, Jan 23 2019
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MATHEMATICA
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Table[Product[k^7+(n-k)^7, {k, 0, n}], {n, 0, 10}]
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PROG
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(PARI) m=7; vector(10, n, n--; prod(k=0, n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019
(Magma) m:=7; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Jan 18 2019
(Sage) m=7; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..10)] # G. C. Greubel, Jan 18 2019
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CROSSREFS
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Cf. 2*A000541 (with sum instead of product).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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